U.S. patent application number 13/465874 was filed with the patent office on 2012-08-30 for ballistic ranging methods and systems for inclined shooting.
This patent application is currently assigned to Bitterroot Advanced Ballistics Research, LLC. Invention is credited to Ted C. Almgren, William T. McDonald.
Application Number | 20120217300 13/465874 |
Document ID | / |
Family ID | 46001990 |
Filed Date | 2012-08-30 |
United States Patent
Application |
20120217300 |
Kind Code |
A1 |
McDonald; William T. ; et
al. |
August 30, 2012 |
Ballistic Ranging Methods and Systems For Inclined Shooting
Abstract
A portable system for facilitating inclined shooting of
projectile weapons comprises a ranging system, an inclinometer and
a processor. The ranging system measures a line-of sight range
distance from a vantage point to a target that is elevated or
depressed relative to the vantage point, and the inclinometer
measures an inclination angle of a line of sight between the
vantage point and the target. Based on information from the
rangefinder and inclinometer, the processor determines a predicted
altitude-compensated inclined shooting (ACIS) trajectory at the
line-of sight range distance for a preselected projectile. The ACIS
trajectory is based on a bullet path height correction between a
bullet path height at a first altitude and a bullet path height at
a second altitude, a range distance of the target from the vantage
point, and selected meteorological atmospheric information.
Inventors: |
McDonald; William T.;
(Darby, MT) ; Almgren; Ted C.; (Darby,
MT) |
Assignee: |
Bitterroot Advanced Ballistics
Research, LLC
Darby
MT
|
Family ID: |
46001990 |
Appl. No.: |
13/465874 |
Filed: |
May 7, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
12952121 |
Nov 22, 2010 |
8172139 |
|
|
13465874 |
|
|
|
|
Current U.S.
Class: |
235/404 |
Current CPC
Class: |
G01C 3/04 20130101; F41G
3/06 20130101; F41G 3/08 20130101; F41G 3/02 20130101 |
Class at
Publication: |
235/404 |
International
Class: |
G06F 19/00 20110101
G06F019/00 |
Claims
1-20. (canceled)
21. A method, comprising: determining a line-of-sight range from a
current vantage point to a target that is elevated or depressed
relative to the current vantage point; determining an inclination
angle of a line of sight between the current vantage point and the
target; and determining a predicted altitude-compensated inclined
shooting trajectory at the line-of-sight range for a preselected
projectile based on a difference in altitude between the current
vantage point with respect to sea level and an altitude of a
sighting-in vantage point with respect to sea level, the
sighting-in vantage point being a vantage point at which a
projectile weapon shooting the preselected projectile was sighted
in.
22. The method according to claim 21, wherein the predicted
altitude-compensated inclined shooting trajectory is based on a
bullet path height correction between a bullet path height at the
current vantage point with respect to sea level and a bullet path
height at the sighting-in vantage point with respect to sea
level.
23. The method according to claim 22, wherein the bullet path
height correction is further based on a range distance to the
target from the current vantage point.
24. The method according to claim 22, wherein the bullet path
height correction is further based on Army Standard Meteorological
Atmosphere information, International Standard Atmosphere
information, or actual atmosphere information.
25. The method according to claim 21, wherein the processor is
further capable of being configured to determine a holdover or a
holdunder corresponding to the predicted altitude-compensated
inclined shooting trajectory.
26. The method according to claim 25, further comprising displaying
information based on the holdover or the holdunder corresponding to
the predicted altitude-compensated inclined shooting
trajectory.
27. The method according to claim 21, further comprising
calculating an angular elevation adjustment for an aiming device
corresponding to the predicted altitude-compensated inclined
shooting trajectory.
28. The method according to claim 27, further comprising displaying
the angular elevation adjustment representing to the predicted
altitude-compensated inclined shooting trajectory.
29. The method according to claim 27, further comprising
communicating to a weapon-aiming device a signal representative of
the angular elevation adjustment corresponding to the predicted
altitude-compensated inclined shooting trajectory.
30. The method according to claim 29, wherein the method is
performed by a weapon-aiming device comprising a rangefinder or a
riflescope, the rangefinder or the riflescope comprising an
automatic elevation adjustment mechanism responsive to the signal
representative of the angular elevation adjustment.
31. An article comprising: a computer readable medium having stored
thereon instructions that, if executed, result in at least the
following: determining a line-of-sight range from a current vantage
point to a target that is elevated or depressed relative to the
current vantage point; determining an inclination angle of a line
of sight between the current vantage point and the target; and
determining a predicted altitude-compensated inclined shooting
trajectory at the line-of-sight range for a preselected projectile
based on a difference in altitude between the current vantage point
with respect to sea level and an altitude of a sighting-in vantage
point with respect to sea level, the sighting-in vantage point
being a vantage point at which a projectile weapon shooting the
preselected projectile was sighted in.
32. The article according to claim 31, wherein the predicted
altitude-compensated inclined shooting trajectory is based on a
bullet path height correction between a bullet path height at the
current vantage point with respect to sea level and a bullet path
height at the sighting-in vantage point with respect to sea
level.
33. The article according to claim 32, wherein the bullet path
height correction is further based on a range distance to the
target from the current vantage point.
34. The article according to claim 32, wherein the bullet path
height correction is further based on Army Standard Meteorological
Atmosphere information, International Standard Atmosphere
information, or actual atmosphere information.
35. The article according to claim 31, wherein the processor is
further capable of being configured to determine a holdover or a
holdunder corresponding to the predicted altitude-compensated
inclined shooting trajectory.
36. The article according to claim 35, further comprising
displaying information based on the holdover or the holdunder
corresponding to the predicted altitude-compensated inclined
shooting trajectory.
37. The article according to claim 31, further comprising
calculating an angular elevation adjustment for an aiming device
corresponding to the predicted altitude-compensated inclined
shooting trajectory.
38. The article according to claim 37, further comprising
displaying the angular elevation adjustment representing to the
predicted altitude-compensated inclined shooting trajectory.
39. The article according to claim 37, further comprising
communicating to a weapon-aiming device a signal representative of
the angular elevation adjustment corresponding to the predicted
altitude-compensated inclined shooting trajectory.
40. The article according to claim 39, wherein the instructions are
executed by a weapon-aiming device comprising a rangefinder or a
riflescope, the rangefinder or the riflescope comprising an
automatic elevation adjustment mechanism responsive to the signal
representative of the angular elevation adjustment.
Description
CROSS-REFERENCE TO RELATED PATENT APPLICATION
[0001] The present patent application is a continuation patent
application of U.S. patent application Ser. No. 12/952,121, by
William T. McDonald et al., entitled "Ballistic Ranging Methods and
Systems For Inclined Shooting," and filed Nov. 22, 2010, the
disclosure of which is incorporated by reference herein.
BACKGROUND
[0002] The subject matter disclosed herein relates to methods and
systems for compensating for ballistic drop and to portable devices
(such as various equipments embodying various target locating and
designators) implementing such methods. More particularly, the
subject matter disclosed herein relates to method and system for
compensating for ballistic drop for inclined shooting and to
rangefinders and other portable devices implementing such
methods.
BRIEF DESCRIPTION OF THE DRAWINGS
[0003] The subject matter disclosed herein is illustrated by way of
example and not by limitation in the accompanying figures in which
like reference numerals indicate similar elements and in which:
[0004] FIG. 1 depicts a schematic diagram of level-fire and
inclined-fire trajectories for a projectile;
[0005] FIG. 2 depicts a schematic diagram illustrating measurements
and factors in calculating an Equivalent Horizontal Range;
[0006] FIG. 3 depicts a flow chart for one exemplary embodiment of
a method for determining the Equivalent Horizontal Range for
accurately aiming a projectile weapon at an elevated or depressed
target located at a inclined line of sight;
[0007] FIG. 4 depicts a summary of one exemplary method for
calculating a trajectory parameter of bullet path and Equivalent
Horizontal Range for bullets;
[0008] FIG. 5 depicts a summary of one exemplary method for
calculating a trajectory parameter of an arrow path and equivalent
horizontal range for arrows
[0009] FIG. 6 depicts a flow diagram for one exemplary embodiment
of operations and a computational process performed by a master
processor for generating reference trajectory information for
computing Altitude-Compensated Inclined Shooting (ACIS) trajectory
information for a selected cartridge according to the subject
matter disclosed herein, the ACIS method being an alternative to
the equivalent horizontal range method for generating reference
trajectory information;
[0010] FIG. 7 depicts a flow diagram for one exemplary embodiment
of operations and computational process performed by a device
processor for generating Altitude-Compensated Inclined Shooting
(ACIS) trajectory information for a selected cartridge according to
the subject matter disclosed herein;
[0011] FIG. 8 depicts an exemplary embodiment of a portable
handheld rangefinder that generates Attitude-Compensated Inclined
Shooting (ACIS) trajectory information for a selected
cartridge;
[0012] FIG. 9 depicts an enlarged view of an exemplary embodiment
of an electronic display as viewed through an eyepiece of the
exemplary portable handheld rangefinder depicted in FIG. 8;
[0013] FIG. 10 depicts an exemplary block diagram for an exemplary
embodiment of rangefinder device according to the subject matter
disclosed herein; and
[0014] FIG. 11 depicts an exemplary embodiment of a telescopic
sighting device for use with the subject matter disclosed
herein.
DETAILED DESCRIPTION
[0015] The word "exemplary," as used herein, means "serving as an
example, instance, or illustration." Any embodiment described
herein as "exemplary" is not to be construed as necessarily
preferred or advantageous over other embodiments. Also, six
technical terms used repeatedly herein require explanation. These
terms are "ballistic path," "bullet path," "arrow path," "ballistic
path height," "bullet path height," and "arrow path height." A
projectile flying through the air without propulsion follows a
ballistic trajectory, which may also be called a "ballistic path."
Two types of projectiles are addressed herein, bullets from
firearms and arrows from bows. Thus, the "ballistic path" of a
bullet is a "bullet path," and similarly, the "ballistic path" of
an arrow is an "arrow path". When the word "height" is added to any
of these terms (e.g., "bullet path height"), it refers specifically
to the perpendicular distance between the instantaneous position of
the projectile (e.g., the bullet) in flight and the extended line
of sight of a shooter through the sighting device on the weapon
which launched the projectile. The path height is considered
positive when the projectile is above the extended line of sight,
and negative when the projectile is below the extended line of
sight.
[0016] FIG. 1 depicts a schematic diagram illustrating the effect
on the trajectory of a projectile of the inclination of the line
along which projectile is fired, cast, or otherwise launched (the
"line of initial trajectory" or, in the case of guns, the "bore
line"). For purposes of illustration, the trajectory curves and
angles between various lines in FIG. 1 are greatly exaggerated and
are not to scale.
[0017] With reference to FIG. 1, a "level fire" trajectory is the
path along which a projectile moves when shot at a target T at
range R.sub.0 and at substantially the same geographic elevation as
a vantage point VP of the shooter. The weapon launching the
projectile has a line of initial trajectory ("level-fire bore
line") that is not actually level, but rather is inclined relative
to the level-fire line of sight (level-fire LOS) by an elevation
angle .alpha.. The angle .alpha. is quite small, typically about
one minute of angle (MoA) for a firearm, and larger (several MoA)
for a bow. The level-fire line of sight, which is therefore
approximately horizontal, begins at a height h above the beginning
of the bore line. The height h and elevation angle .alpha.
represent the typical mounting arrangement of a sighting device
(i.e., riflescope, open sights, etc.) on a firearm or an archery
sight on a bow. The level-fire trajectory intersects the level-fire
line of sight at range R.sub.0 and is known as the "sighted-in
range" or "zero range" or "zeroed-in range" (also referred to
herein as zero-range distance R.sub.Z) of the weapon and sight
combination. The sighted-in range R.sub.0 is typically established
by shooting the weapon at a target at a known horizontal reference
distance R.sub.0, such as 100 yards, and adjusting the elevation
angle .alpha. of the riflescope or other sighting device until
projectiles shot by the weapon impact the target at .alpha. point
that coincides with the cross hairs or other aiming mark of the
riflescope or other sighting device.
[0018] An "inclined-fire trajectory" is also depicted in FIG. 1.
The inclined-fire trajectory represents the path along which the
same projectile travels when aimed at a target that is elevated
relative to vantage point VP. The height h and elevation angle
.alpha. of the inclined-fire line of sight relative to the bore
line are the same as in the level-fire scenario, because there can
be no adjustment to the sighting device on the firearm or bow to
anticipate the target elevation in the field. The inclined-fire
line of sight will be inclined by an angle of inclination .theta..
As illustrated in FIG. 1, the inclined-fire trajectory crosses the
inclined-fire line of sight at a distance substantially greater
than the sighted-in range R.sub.0. This overshoot is due to the
effect of gravity, which always acts in the vertically downward
direction, regardless of the angle of inclination .theta.. The
overshoot phenomena and prior methods of correcting for it are
discussed in detail by W. T. McDonald in his paper titled "Inclined
Fire" (June 2003), available from sierrabullets.com. The effects of
inclination are typically even more pronounced in archery than for
bullets and are caused by differences in the initial speed and
aerodynamic characteristics of the projectiles used. The
line-of-sight range distance and the inclination angle of a target
relative to the shooter may be measured or estimated in the field
where the target is encountered.
[0019] In accordance with exemplary embodiments described herein,
many hunters (including bow hunters) and other shooters, such as
military and law enforcement snipers, are versed in holdover
techniques for compensating for ballistic drop in horizontal fire
scenarios. A holdover adjustment involves aiming high by a measured
or estimated amount. For example, a countersniper shooting a rifle
with a riflescope sighted in at 200 yards may know that a killing
shot for his target (in the heart-lung area) at a level-fire range
of approximately 375 yards involves aiming the cross hairs of the
riflescope at the top of the target's head. Holdover adjustments
are much faster in practice than elevation adjustments, which
involve manually adjusting an elevation setting of the riflescope
or other aiming device to change the elevation angle .alpha. of the
aiming device relative to the weapon. Holdover adjustments are also
the primary mode of aiming adjustment for most archers. Holdover
and holdunder techniques also avoid the need to re-zero the aiming
device after making a temporary elevation adjustment.
[0020] Many varieties of ballistic reticles are employed in
riflescopes to facilitate holdover and holdunder. For archery, a
common ballistic aiming sight, known as a pin sight, is often
employed for holdover aiming adjustment. Ballistic reticles and
other ballistic aiming sights generally include multiple aiming
marks spaced apart along a vertical axis. Exemplary ballistic
reticles include mil-dot reticles and variations, such as the
LEUPOLD TACTICAL MILLING RETICLE.TM. (TMR.TM.) available from
Leupold & Stevens, Inc., Leupold.RTM. DUPLEX.TM. reticles; the
LEUPOLD SPECIAL PURPOSE RETICLE.TM. (SPR.TM.); and LEUPOLD
BALLISTIC AIMING SYSTEM.TM. (BAS.TM.) reticles, such as the LEUPOLD
BOONE & CROCKETT BIG GAME RETICLE.TM. and the LEUPOLD VARMINT
HUNTER'S RETICLE.TM. BAS reticles and methods of using them are
described in U.S. Pat. No. 7,603,804 B2 to Zaderey et al., entitled
"Ballistic Reticle for Projectile Weapon Aiming Systems and Method
of Aiming" ("the '804 patent"), the disclosure of which is
incorporated herein by reference. As described in the '804 patent,
BAS reticles include secondary aiming marks that are spaced at
progressively increasing distances below a primary aiming mark and
positioned to compensate for ballistic drop at preselected regular
incremental ranges for a group of ammunition having similar
ballistic characteristics.
[0021] In accordance with one exemplary embodiment depicted in
FIGS. 2 and 3, a method 300 of inclined shooting involves
calculation of an equivalent horizontal range (EHR) that may be
used by a shooter to make a holdover or elevation adjustment for
accurately aiming a projectile weapon at an elevated or depressed
target located at a inclined line-of-sight (LOS) range that is
different from the EHR. With reference to FIG. 2, a shooter at
vantage point VP determines a line-of-sight range to a target. As
in FIG. 1, a zero range R.sub.0 represents the horizontal-fire
distance at which the trajectory of the projectile launched from
the projectile weapon and the line of sight from the aiming device
of the weapon intersect. Line-of-sight ranges R.sub.1 and R.sub.2
to two different targets are depicted in FIG. 2, illustrating the
usefulness of the method with respect to both positive and negative
ballistic path heights BP.sub.1 and BP.sub.2 relative to the
inclined-fire LOS. For purposes of illustration, the steps of
method 300 (FIG. 3) will be described with reference to a generic
LOS range R to a target T, shown in FIG. 2 at range R.sub.2. It
should be appreciated that the methods described herein are equally
applicable to "near" LOS ranges R.sub.1 at which the ballistic path
height BP.sub.1 is positive, as well as to "far" LOS ranges R.sub.2
at which the ballistic path height BP.sub.2 is negative. The LOS
range R may be determined by a relatively accurate ranging
technique, such as use of a lidar (laser ranging) or radar, or by a
method of range estimation, such as optical range estimating
methods in which a distant target of known size is bracketed in a
scale of an optical device, as described in the '804 patent.
[0022] Methods 300 in accordance with the present disclosure also
involve determining an inclination .theta. of the inclined LOS
between vantage point VP and the target F. The angle of inclination
.theta. may be determined by an electronic inclinometer, calibrated
tilt sensor circuit, or other similar device. For accuracy, ease of
use, and speed, an electronic inclinometer for determining the
angle of inclination .theta. may be mounted in a common housing
with a handheld laser rangefinder 800 of the kind described below
with reference to FIGS. 8-10.
[0023] FIG. 3 is a flow diagram depicting steps of inclined
shooting method 300, including the initial steps of determining the
LOS range R (step 312) and determining the inclination .theta. of
the inclined LOS (step 314). With reference to FIG. 3, after LOS
range R and inclination .theta. have been determined (steps 312 and
314), method 300 may involve a check (step 316) to determine
whether the absolute value of inclination .theta. is less than a
predetermined limit under which the effects of inclination can be
disregarded and the LOS range R can be regarded as the Equivalent
Horizontal Range (EHR) (step 318).
[0024] Archery ballistics exhibit a more significant difference
between positive and negative lines of initial trajectory (uphill
and downhill shots) because the initial velocity is relatively low,
giving the effects of gravity more time to affect the trajectory
over a given distance than with bullets, which reach their targets
much faster than arrows. Especially at long ranges, uphill shots
experience more drop than downhill shots; therefore, when applying
method 300 for archery, check 316 may involve comparing a positive
inclination .theta. against a positive limit and a negative
inclination .theta. against a negative limit that is different from
the positive limit. Mathematically, such a check would be expressed
as: {lower_limit}>.theta.<{upper_limit}?
[0025] If the result of check 316 is negative, then a predicted
trajectory parameter TP is calculated or otherwise determined at
the LOS range for a preselected projectile P shot from vantage
point VP toward the target T (step 320). Trajectory parameter TP
may comprise any of a variety of trajectory characteristics or
other characteristics of a projectile that are calculable using
ballistics software. For example, trajectory parameter TP at LOS
range R may comprise one or more of ballistic path height (e.g.,
arrow path or bullet path), ballistic drop relative to line of
initial trajectory (e.g., the bore line in FIG. 1), observed
ballistic drop perpendicular to LOS (i.e., (vertical ballistic
drop) cos(.theta.+.alpha.)), velocity, energy, and momentum. In
accordance with the exemplary embodiment described below with
reference to FIGS. 2 and 4, for R=R.sub.2, trajectory parameter TP
may comprise ballistic path height BP.sub.2 (e.g., bullet path
height). In another embodiment, described below with reference to
FIG. 5, the trajectory parameter of ballistic path height comprises
arrow path height (AP).
[0026] Nothing in the figures or written description should,
however, be construed as limiting the scope of possible trajectory
parameters to only ballistic path height. Of the many possible
choices of trajectory parameters, ballistic path height (bullet
path height or arrow path height) usually is best for the shooter,
who needs to know where the projectile will be relative to the line
of sight when the projectile reaches the line-of-sight range
distance to the target so that the shooter can make appropriate
aiming adjustments.
[0027] After the trajectory parameter TP has been calculated, the
method may then output the trajectory parameter TP (step 321) or
calculate EHR based on the trajectory parameter TP or parameters
(step 322). At step 321, the trajectory parameter TP output may
comprise ballistic path height BP expressed as a linear distance in
inches or millimeters (mm) of apparent drop, or as a corresponding
angle subtended by the ballistic path height (e.g., BP.sub.2 in
FIG. 2) in minutes of angle (MOA) or milliradians (mils). The TP
output (step 321) may comprise a display of numerical ballistic
path data in an electronic display device, such as a display 900
(FIG. 9) of rangefinder 800 (FIG. 8) or a reticle in a riflescope.
Alternatively or additionally, the TP output (step 321) may
comprise a graphical display of a holdover aiming recommendation in
a rangefinder display, a riflescope reticle, an archery sight, or
another aiming sight, based on the trajectory parameter of
ballistic path height BP.
[0028] In one exemplary method of calculating EHR, a reference
ballistics equation for a level-fire scenario (.theta.=0)
comprising a polynomial series is reverted (i.e., through series
reversion) to solve for EHR based on a previously calculated
ballistic path height BP (BP.sub.2). As depicted in FIG. 2,
BP.sub.2 corresponds to EHR.sub.2 under level-fire conditions.
Thus, EHR is calculated as the range at which trajectory parameter
TP would occur if shooting projectile P in a level-fire condition
from the vantage point VP toward a theoretical target T.sub.th in a
common horizontal plane with vantage point VP, such that the
horizontal plane coincides with the level-fire LOS. The reference
ballistics equation may be established to deviate slightly from
horizontal without appreciable error. Consequently, the terms
"horizontal," "level-fire LOS," and other similar terms are
construed to allow for equations to deviate from perfect horizontal
unless the context indicates otherwise. For example, when solving
for EHR, the degree of levelness of the reference equations should
facilitate calculation of EHR with sufficient accuracy to allow
aiming adjustments for inclined shooting resulting in better than
.+-.6 inches of error at 500 yards throughout the range of between
-60 and +60 degrees inclination. Ballistic trajectories are
generally flatter at steeper shooting angles and trajectories of
different projectiles are therefore more similar. Consequently, the
deviation tends to be less significant at very steep inclines.
[0029] The calculation of trajectory parameter TP, the calculation
of equivalent horizontal range EHR, or both, may also be based on a
ballistic coefficient of the projectile P and one or more shooting
conditions. The ballistic coefficient and shooting conditions may
be specified by a user or automatically determined at step 324.
Automatically-determined shooting conditions may include
meteorological conditions, such as temperature, relative humidity,
and/or barometric pressure, which may be measured by micro-sensors
in communication with a computer processor for operating method
300. Meteorological conditions may also be determined by receiving
local weather data via radio transmission signal, received by an
antenna and receiver in association with the computer processor.
Similarly, geospatial shooting conditions, such as the compass
heading of the LOS to the target and the geographic location of the
vantage point VP (including latitude, longitude, altitude, or all
three), may be determined automatically by a GPS receiver and an
electronic compass sensor in communication with the computer
processor, to ballistically compensate for the Coriolis effect
(caused by the rotation of the Earth). Alternatively, such
meteorological and geospatial shooting conditions may be specified
by a user and input into a memory associated with the computer
processor, based on observations made by the user. It may be noted
that for bows, geospatial conditions are unnecessary because
maximum range distances are short, while for high-powered rifles,
Coriolis corrections to a trajectory are necessary only if range
distances exceed about 1000 yards or meters.
[0030] User selection of shooting conditions and ballistic
coefficient may also involve preselecting or otherwise inputting
non-meteorological and non-geospatial conditions for storage in a
memory associated with a computer processor on which method 300 is
executed. The ballistic coefficient and certain shooting
conditions, such as the initial velocity of projectile P (e.g.,
muzzle velocity, in the case of bullets), may be set by a user
simply by selecting from two or more weapon types (such as guns and
bows), and from two or more ballistic groupings and possibly three,
four, five, six, seven or more groups, such that each group has a
nominal ballistic characteristic representative of different sets
of projectiles having similar ballistic properties. The sets
groups) may be mutually-exclusive or overlapping (intersecting). A
sighted-in range of a weapon aiming device and a height of the
weapon aiming device above a bore line of a weapon may also be
entered in this manner. In a rangefinder device 800 for operating
the method, described below with reference to FIGS. 8 and 9, the
weapon type and ballistic group may be selected from a menu of
possible choices during a menu mode or setup mode of rangefinder
device 800.
[0031] After a trajectory parameter TP has been calculated at step
320 or EHR has been calculated at step 322, method 300 then
involves outputting TP or EHR in some form (step 321 or 326). For
example, TP or EHR may be displayed via a display device, such as
an LCD display, in the form of a numeric value specified in a
convenient unit of measure. For example, TP output may be expressed
as ballistic path height BP in inches or mm of apparent drop or as
an angle (in MOA or mils) subtended by the ballistic path height
BP. EHR may be expressed in yards or meters, for example. In other
embodiments, BP or EHR may be effectively output via a graphical
representation of the data through the identification of a reticle
aiming mark corresponding to the holdover or holdunder (holdover or
holdunder is always the negative of the BP), or the EHR, for
example, as described below.
[0032] Once EHR is output at 326, EHR can then be employed to aim
the projectile weapon at target T (step 328) along the inclined LOS
at R.sub.2. In one embodiment, a shooter merely makes a holdover or
holdunder adjustment based on the calculated EHR, as if he or she
were shooting under level-fire conditions--it being noted that wind
effects, firearm inaccuracy, and wiggle of the shooter are still in
effect over the entire LOS range R.sub.2. In another embodiment,
the shooter adjusts an elevation adjustment mechanism of a
riflescope or other aiming device based on the displayed EHR.
Similar elevation adjustments may be made based on the display of
the calculated trajectory parameter TP (step 321).
[0033] FIG. 4 summarizes details of one possible sequence of steps
400 for calculating a trajectory parameter of bullet path height
(BP) and equivalent horizontal range (EHR) for bullets. The
calculation sequence 400 begins with selection of a ballistic group
(A, B, or C) in which the bullet and cartridge are listed (step
401). Ballistic grouping may effectively normalize groups of
bullets having similar characteristics, based on their ballistic
coefficients, muzzle velocities and masses. Listings of cartridges
in the various groupings may be provided to the user by a printed
table or software-generated information display, facilitating
selection of the appropriate ballistic group. Reference
trajectories for ballistic groups A, B, and C are set forth in
Table 1. The other inputs to the calculations include the LOS range
R and the inclination angle .theta., which may be determined
automatically by a handheld laser rangefinder with inclinometer
(step 402). The calculation method involves solving the following
polynomial equation for bullet path height BP:
BP=a.sub.0+a.sub.1R+a.sub.2R.sup.2+a.sub.3R.sup.3+a.sub.4R.sup.4
(1)
[0034] (step 406), in which the coefficients a.sub.0, a.sub.1,
a.sub.2, a.sub.3 and a.sub.4 are calculated from the inclination
angle .theta. based on a series of polynomial equations 404 in
which the coefficients thereof (identified in FIG. 4 as A.sub.00,
A.sub.01, A.sub.02, etc.) are different stored parameters for each
ballistic group A, B, and C. A single equation 406 (Equation (1))
is suitable for both positive and negative angles of inclination,
expressed as absolute angular values. After bullet path height BP
has been determined, the BP is then used as an input to one of two
different reversions of the bullet path equation for .theta.=0 to
solve for EHR. If bullet path height BP is positive (test 408),
then a "short-range EHR" polynomial equation is used (step 410),
such that B.sub.0, B.sub.1, . . . , B.sub.6 are parameters
corresponding to the selected ballistic group. If BP is negative
(test 408), then a "long-range EFIR" polynomial equation is used
(step 412), such that C.sub.0, C.sub.1, . . . , C.sub.6 are
parameters corresponding to the selected ballistic group. Each
ballistic group also has an associated coefficient named BPLIM,
which is an upper limit for BP in the computations shown in FIG. 4.
Parameters A.sub.00 to A.sub.43, B.sub.0 to B.sub.6, and C.sub.0 to
C.sub.6 are constants that are stored for each of the ballistic
groups and recalled based on the selected ballistic group for
purposes completing the calculations 400.
[0035] FIG. 5 illustrates a similar sequence of calculations 500
for archery. In FIG. 5, reference numerals 501, 502, 506, etc.,
indicate steps that respectively correspond to steps 401, 402, 406,
etc., of FIG. 4. Unlike the calculations 400 (FIG. 4) for bullets,
the calculation of ballistic path for arrows 500 (hereinafter arrow
path (AP) must take into account whether the inclination angle is
positive or negative (branch 503), due to the increased flight time
of arrows and attendant increased effects of gravity on their
trajectory. For this reason, the calculations involve one of two
different sets of coefficients A.sub.ij and D.sub.ij, (for 3, 4, 5
and j=1, 2, 3, 4, 5) depending on whether the inclination is
positive ((step 504a') or negative (step 504b'). Parameters
A.sub.00 to A.sub.43, B.sub.0 to B.sub.6, C.sub.0 to C.sub.6,
D.sub.00 to D.sub.43, APLIM, and EHRLIM are constants that are
stored in memory for each of the ballistic groups and recalled
based on the selected ballistic group for purposes completing the
calculations 500.
[0036] Table 1 lists one example of criteria for ballistic grouping
of arrows and bullets:
TABLE-US-00001 TABLE 1 BALLISTIC CHARACTERISTIC GROUP BALLISTIC
DROP (WITHOUT INCLINE) Arrow group A Arrow drop of 20-30 in from
the 20 yd sight pin at 40 yd Arrow group B Arrow drop of 30-40 in
from the 20 yd sight pin at 40 yd Arrow group C Arrow drop of 10-20
in from the 20-yd sight pin at 40 yd Bullet group A Rifles sighted
in at 200 yards with 30-40 in drop at 500 yd Bullet group B Rifles
sighted in at 200 yards with 40-50 in drop at 500 yd Bullet group C
Rifles sighted in at 300 yards with 20-30 in drop at 500 yd
[0037] Arrow groupings may be more dependent on the launch velocity
achieved than the actual arrow used, whereas bullet groupings may
be primarily based on the type of cartridge and load used. Table 2
lists exemplary reference trajectories from which the calculation
coefficients of FIG. 4 may be determined for ballistic groups A, B,
and C.
TABLE-US-00002 TABLE 2 BALLISTIC GROUP REFERENCE TRAJECTORY A
Winchester Short Magnum with Winchester 180 grain Ballistic
Silvertip bullet at 3010 fps, having a level fire bullet path
height of -25.21 in at 500 yds. B 7 mm Remington Magnum with
Federal 150 grain SBT GameKing bullet at 3110 fps, having a level
fire Bullet Path height of -34.82 in at 500 yds. C 7 mm-08
Remington with Remington Pointed Soft Point Core-Lokt bullet at
2890 fps, having a level fire Bullet Path height of -45.22 in at
500 yds.
[0038] Alternatives to solving a series of polynomial equations
also exist, although many of them will not provide the same
accuracy as solving a polynomial series. For example, a single
simplified equation for ballistic drop or ballistic path height may
be used to calculate a predicted trajectory parameter, and then a
second simplified equation used to calculate EHR from the predicted
trajectory parameter. Another alternative method of calculating EHR
involves the "Sierra Approach" described in W. T. McDonald,
"inclined Fire" (June 2003), incorporated herein by reference.
Still another alternative technique for calculating ballistic drop
or ballistic path involves a table lookup of a predicted trajectory
parameter and/or interpolation of table lookup results, followed by
calculation of EHR using the formula identified in FIG. 4. Yet
another alternative involves determining both the predicted
trajectory parameter and EHR by table lookup and interpolation,
using stored sets of inclined-shooting data at various angles.
[0039] Table 3 illustrates an example of an EHR calculation using
the sequence of steps for calculating a trajectory parameter of
bullet path height (BP) and equivalent horizontal range (EHR) for
bullets described above in connection with FIG. 4. The EHR
calculations in Table 3 are also compared with the results of
aiming using EHR to aiming with no compensation for incline, and
aiming by utilizing the horizontal distance to the target
(rifleman's rule).
TABLE-US-00003 TABLE 3 .300 WSM, 165 GRAIN NOSLER PARTITION, 3050
FPS MUZZLE LOAD VELOCITY Angle of inclination 50.degree. Inclined
line-of-sight range 500 yds Equivalent Horizontal Range (EHR) 389
yds Ballistic table holdover for 389 yds 18 in level fire
Horizontal leg of the triangle 321 yds Ballistic table holdover for
321 yds 8.5 in Error if horizontal leg is used -9.5 in Ballistic
table holdover for 500 yds 39.5 in level fire (no compensation for
incline) Error if no compensation for incline +21.5 ins
[0040] The subject matter disclosed herein also provides a
technique for determining highly accurate trajectories for inclined
shooting that accounts for effects to a trajectory caused by
altitude. That is, the subject matter disclosed herein also
provides a technique for determining highly accurate
Altitude-Compensated Inclined Shooting (ACIS) trajectories.
According to the subject matter disclosed herein, ACIS trajectories
are determined for a specific cartridge type at all target range
distances within the maximum effective range of the cartridge, at
all positive and negative target inclination angles within .+-.70
degrees, and at all altitudes above sea level up to a practical
maximum for first zeroing-in the firearm and then later firing (at
a different altitude) at a target encountered in the field.
Additionally, the ACIS trajectories provide a full
3-degree-of-freedom analytical model for trajectory calculations.
Moreover, the firearm may be a machine gun, rifle, or handgun using
that specific cartridge type. The exemplary ACIS method described
herein is described for firearms that shoot bullets. The ACIS
method also may be applied to bows shooting arrows, although some
modifications are necessary because, as explained above, an arrow
trajectory for shooting upward at a positive inclination angle
differs from the trajectory for shooting downward at a negative
inclination angle of the same value, which is caused by lower
velocities and longer times of flight for arrows over a given
distance,
[0041] The computational procedure for ACIS trajectories utilizes
characteristics of known firearm and ammunition, such as projectile
ballistic coefficient(s) available from manufacturers' data or
other test data, and the muzzle velocity of the firearm.
Additionally, the computational procedure utilizes standard
meteorological conditions, i.e., standard atmospheric pressure,
temperature, and relative humidity versus altitude, which are
available from the Army Standard Meteorological Atmosphere ("Army
Standard Metro") at the particular altitude at which the firearm is
sighted-in (zeroed-in) and at the particular altitude of the firing
point in the field. For Army Standard Metro information, see, for
example, "Modern Exterior Ballistics," R. L. McCoy, Schiffer
Military History, 1999, page 166; "Exterior Ballistics of Small
Arms Projectiles," E. D. Lowry, Olin Mathiesin Chemical
Corporation, 1965, page 74; and "Sierra Rifle Reloading Manual,"
3.sup.rd Edition, Sierra Bullets L. P., 1989, pages 480-481). The
Army Standard Metro atmosphere is the reference for the standard
drag functions G1, G5, G6, G7, etc., and the ballistic coefficient
value(s) pertaining to each of those drag functions and,
consequently, is the reference atmosphere for almost all predictive
ballistic computations. Other possibilities exist for atmospheric
conditions, such as the International Standard Atmosphere (ISA) or
even absolute measurements of temperature, pressure, and humidity
at the shooting location, but the Army Standard Metro Atmosphere
has been adopted for predictive ballistic computations with
commercial ammunition. Altitude information above sea level at the
zeroing-in site and at the firing site is obtained from reference
data, field measurements, topographical maps, etc. Target
conditions (i.e., target direct-range distance and target
inclination angle relative to the firing point) are obtained from
measurements made in real time when a target is encountered in the
field. Winds are not considered because wind conditions,
particularly at the firing location, cannot be accurately predicted
in advance. Consequently, when a shooter is using trajectory
information provided by the computational procedure disclosed
herein, the experience of the shooter must be relied on to correct
for wind conditions when a target is encountered in the field.
[0042] In one exemplary, embodiment, the computational technique
disclosed herein utilizes two different computer processors, such
as a relatively high-numerical-precision computer processor
(referred to herein as a "master processor") and a relatively
low-numerical-precision computer processor (referred to herein as a
"device processor"). The master processor is used to pre-compute
reference trajectory information that is later used by the device
processor to provide near real-time (1 second or less)
Altitude-Compensated Inclined Shooting (ACAS) trajectory
information in the field. Exemplary embodiments of the master
processor comprise, but are not limited to, a Personal Computer
(PC) or a handheld Personal Digital Assistant (PDA) having
ballistics software capable of computing a highly accurate
projectile trajectory. Exemplary embodiments of a device processor
comprise, but are not limited to, a computer processor device
having a limited computation capacity, such as a device mounted to
a firearm or a handheld device used by a shooter or a companion of
the shooter. In an alternative exemplary embodiment, a single
computer processor comprising sufficient computing capability may
be used in place of two different computer processors. An exemplary
embodiment of such a single computer processor comprises, but is
not limited to, a handheld Personal Digital Assistant (PDA) having
ballistics software capable of computing a highly accurate
projectile trajectory. It should understood that the computer
processors referred to herein generally include components and
capability for providing functionality, such as, but not limited
to, input/output (I/O), storage, power, etc.
[0043] Because the trajectory information provided by the
computational procedure applies to a single cartridge, the memory
storage requirement of the device processor for each cartridge is
relatively modest because only reference trajectory information for
the particular cartridge needs to be stored for the device
processor. If reference trajectory information for multiple
cartridges is desired, the reference trajectory information for
each desired cartridge is generated by the master processor by
repeating the computational procedure for each desired cartridge
and then transferring the different reference trajectory
information for each cartridge to the device processor. Memory
requirements for the device processor would accordingly increase
based on the number of desired cartridges. In the field, the
reference trajectory information is then accessed by an operator
through the device processor. The computational procedure performed
by the device processor for determining an ACIS trajectory is the
same regardless which cartridge is being used.
[0044] In an alternative exemplary embodiment, all computations are
performed by a master-processor-type computer processor, such as a
handheld Personal Digital Assistant (PDA) having ballistics
software capable of computing a highly accurate projectile
trajectory. For this alternative exemplary embodiment, reference
trajectory information is computed prior to firing in the field,
and then accessed in the field for computing an ACIS trajectory for
a selected cartridge.
[0045] FIG. 6 depicts a flow diagram 600 for one exemplary
embodiment of operations and a computational process performed by a
master processor for generating reference trajectory information
for computing Altitude-Compensated Inclined Shooting (ACS)
trajectory information for a selected cartridge. Computations are
initiated at 601 by, for example, a user inputting and/or selecting
from a menu the initial data comprising (1) the specific projectile
for which the computations will be performed; (2) the ballistic
coefficient(s) for the projectile and the projectile speed range
within which each ballistic coefficient value applies; (3) the
muzzle velocity (i.e., the speed of the projectile when the
projectile leaves the muzzle of the firearm); (4) the zero-range
distance for which the firearm has been or will be sighted-in; (5)
the maximum range distance for which trajectory computations are to
be performed (normally the maximum effective range distance for the
cartridge); (6) the range-distance increment (RDI) (e.g., 50 yards
or meters for a high powered cartridge) at which trajectory
parameters will be outputted, listed, and/or stored for the
projectile; (7) the sight height of the firearm (i.e., the
perpendicular distance of the line of sight through the sighting
device on the firearm above the bore centerline; and (8) the
physical units in which trajectory parameters will be expressed
(i.e., all English units, all metric units, or "mixed" units in
which range distances are expressed in meters and all other
parameters are expressed in English units). The following
description uses English units, but it should be understood that
metric or mixed units could also be used.
[0046] At 602, the Army Standard Meteorological conditions are
selected for all computations that will be performed. In one
exemplary embodiment, the Army Standard Metro conditions are
preloaded into the master processor before computations can begin.
In another exemplary embodiment actual atmospheric conditions can
be selected and, for example, manually entered when atmospheric
conditions can be practically predicted in advance of going into
the field. At sea level, the meteorological conditions are 750 mm
(29.5275 in) of mercury atmospheric pressure, 15C (59F) atmospheric
temperature, and 78% relative humidity. The pressure and
temperature at higher altitudes decrease in accordance with tables
listed in the publications referred to previously. The value of
relative humidity normally is not changed as altitude changes
because relative humidity has a small effect on air density at sea
level, and as altitude increases, the vapor pressure of water in
the atmosphere decreases, leading to an even smaller effect caused
by relative humidity. A standard value of gravitational
acceleration of 32.174 ft/sec.sup.2 adjusted for altitude at the
firing point is also used in all computations.
[0047] At 603, a baseline trajectory is computed for the selected
projectile. The baseline trajectory is a level-fire
(zero-inclination angle) trajectory at sea-level standard
conditions between the muzzle of the firearm and the maximum-range
distance (entered at 601). The parameter of interest is the Bullet
Path Height (BPH) of the projectile versus range distance from the
muzzle. BPH is defined herein as the perpendicular distance of the
projectile from the extended line of sight through the sighting
device on the firearm. It should be understood that BPH is not the
Drop of the projectile. For a level-fire trajectory, Drop is
defined herein as the distance of the bullet from a level line
between the muzzle of the firearm and a target located in a level
plane with the firearm. As defined herein, BPH is positive when the
projectile is above the line of sight and negative when the
projectile is below the line of sight. The positive or negative
sign of BPH allows an operator to know where the projectile will
pass with respect to the extended line of sight through the
sighting device on the firearm.
[0048] Both BPH and Drop are routinely calculated by software that
computes trajectories for projectiles in fast and high
numerical-precision computers, such computer processors like the
master processor. An example of such software is the Sierra
Infinity software, which is available from Sierra Bullets, Sedalia,
Mo. For a level-fire trajectory, BPH and Drop at any given range
distance are related by an algebraic equation so that only one
variable need be known for the purposes of the computational
process disclosed herein. For illustrative purposes, BPH is used in
the following description. The zero-range distance R.sub.Z selected
for the firearm and the Drop D.sub.Z, at that specific range
distance are stored in the master processor for later transfer to
the device processor.
[0049] At 604, having BPH versus range distance at selected ranges
(e.g., every 50 yards) between the muzzle of the firearm and the
maximum-range distance, the master computer fits (either internally
or by using a separate external software program) a polynomial
expression to the BPH versus range distance, such as by using the
least squares method of fit. According to one exemplary embodiment,
the standard deviation of the fit should be no greater than 0.5
inch. In one exemplary embodiment, a seventh-order polynomial is
sufficient for most projectile trajectories. If the trajectory is
very flat, a lower-order polynomial could be sufficient. For
trajectories that are more steeply curved, especially near the end
of the trajectory, or to reduce the number of terms in the fit
polynomials to simplify the computations, sequential sectors of the
trajectory may be specified, and a different fit polynomial may be
used in each sector. In one exemplary embodiment, no more than
three sectors are necessary, but in alternative exemplary
embodiments, a greater or lesser number of sectors could be used
without restriction. For a seventh-order polynomial, the reference
Bullet Path (BP) polynomial for any sector will be:
BP(R)=a.sub.i0+a.sub.i1R+a.sub.i2R.sup.2+a.sub.i3R.sup.3+a.sub.i4R.sup.4-
+a.sub.i5R.sup.5+a.sub.i6R.sup.6+a.sub.i7R.sup.7 (2)
in which, i is an index indicating the trajectory segment of the
fit (i=1, 2, or 3); and R is the range distance.
[0050] In one exemplary embodiment, the summation is over all eight
terms in the polynomial expansion. In an alternative exemplary
embodiment, the summation is over fewer terms of the polynomial
expansion. The polynomial fit operation yields the eight (or fewer)
coefficients a.sub.ij in which j=0, 1, 2, . . . , 7) of the
polynomial fit in each sector of the baseline trajectory. The
coefficients a.sub.ij are stored for subsequent transfer to the
device processor. In the explanation that follows, the
seventh-order polynomial of Equation (2) will be used.
[0051] At 605, the next group of computations performed by the
master processor takes place at a specific set of range distances
from the firearm, that is, at each range-distance increment (RDI)
between the maximum range distance of the trajectory back to a
range distance that is one range-distance increment RDI beyond the
zero-range distance R.sub.Z of the firearm. For example, if the
maximum range distance is 800 yards, the R.sub.Z is 200 yards, and
the RDI is 50 yards, trajectory calculations take place at range
distances of 800, 750, 700, 650, 600, . . . , down to 250 yards,
resulting in calculations at twelve specific range distances. The
specific range distances are designated by R.sub.k in the following
explanation. At each such specific range distance, the master
processor uses the specified zero-range distance R.sub.Z with no
adjustment in sight settings to compute the BPH for shooting at sea
level altitude, at 2000 feet above sea level (ASL), at 4000 feet
ASL, at 6000 feet ASL, at 8000 feet ASL, at 10000 ASL, and at 12000
feet ASL. The trajectory calculated for shooting at sea level is
used as the baseline reference trajectory. This observation is
crucial; the shooter always uses a specific value of zero-range
distance R.sub.Z (e.g., 200 yards) regardless of the altitude at
which he or she zeroes-in the firearm.
[0052] The maximum shooting altitude anticipated for zeroing-in
and/or shooting in the field is selected for the present
explanation to be 12000 feet ASL. It should be understood that in
an alternative exemplary embodiment, the maximum shooting altitude
could be selected to be different from 12000 feet ASL, in which
case the maximum altitude would be appropriately adjusted for the
anticipated shooting situation in the field. Normally, for
practical reasons one exemplary embodiment of the software in the
master processor will be limited to a maximum altitude of 15000
feet ASL. For the present exemplary embodiment, an altitude
separation of 2000 feet is used. It should be understood that in an
alternative exemplary embodiment, a different altitude separation
could be used, such as a value that is less than 2000 feet, in yet
another exemplary embodiment, the attitude separation value could
vary, that is, not be a constant value.
[0053] The computations at 605 result in a set of seven (or fewer
depending on the maximum shooting altitude and the altitude
separation value) Bullet Path (BP) values at each range distance
from one range-distance increment (RDI) beyond R.sub.Z out to the
maximum range specified for the projectile. Note that no polynomial
fits are required for the trajectories computed at 605. The results
of the computations are a set of seven (or fewer) Bullet Path (BP)
values at each specific range distance R.sub.k chosen for the
evaluation. Each such computation is based on zeroing-in
(sighting-in) the firearm at sea level and then shooting at each
altitude of the list without any sight changes to compensate for
the altitude changes.
[0054] At 606, the master processor calculates a set of BPH
Corrections at each specific range distance R.sub.k and each
altitude. This is done by designating the BPH for each range
distance R.sub.k, at sea level and at each altitude above sea level
(ASL) as:
BP.sub.0(R.sub.k)=BPH at R.sub.k fired at sea level;
BP.sub.2000(R.sub.k)=BPH at R.sub.k fired at 2000 feet ASL;
BP.sub.4000(R.sub.k)=BPH at R.sub.k fired at 4000 feet ASL;
BP.sub.6000(R.sub.k)=BPH at R.sub.k fired at 6000 feet ASL;
BP.sub.8000(R.sub.k)=BPH at R.sub.k fired at 8000 feet ASL;
BP.sub.10000(R.sub.k)=BPH at R.sub.k fired at 10000 feet ASL;
and
BP.sub.12000(R.sub.k)=BPH at R.sub.k fired at 12000 feet ASL.
(3)
[0055] The left side of Equations (3) are the Ballistic Path
Heights for trajectories in which the firearm is sighted-in at sea
level, then later fired at the specified altitudes and evaluated at
the range distance R.sub.k. The Bullet Path Height Correction
BPcorr(R.sub.k) at range distance R.sub.k and at each altitude is
given by the following arithmetic operations of Equation (4):
BPcorr.sub.0(R.sub.k)=0;
BPcorr.sub.2000(R.sub.k)=BP.sub.2000(R.sub.k)-BP.sub.0(R.sub.k);
BPcorr.sub.4000(R.sub.k)=BP.sub.4000(R.sub.k)-BP.sub.0(R.sub.k);
BPcorr.sub.6000(R.sub.k)=BP.sub.6000(R.sub.k)-BP.sub.0(R.sub.k);
BPcorr.sub.8000(R.sub.k)=BP.sub.8000(R.sub.k)-BP.sub.0(R.sub.k);
BPcorr.sub.10000(R.sub.k)=BP.sub.10000(R.sub.k)-BP.sub.0(R.sub.k);
BPcorr.sub.12000(R.sub.k)=BP.sub.12000(R.sub.k)-BP.sub.0(R.sub.k);
(4)
[0056] As shown by Equation (4), the Bullet Path Height Correction
BPcorr at each firing altitude and at the specific range distance
R.sub.k is the difference between the BPH at which the projectile
is fired and the BPH of the projectile when sighted-in at sea
level. The Bullet Path Height Correction BPcorr is applied to the
Bullet Path Height BPH of the reference trajectory at the range
distance R.sub.k. If the projectile were to be fired at sea level,
the correction for altitude would be zero at all range distances
because the reference trajectory is the actual trajectory at that
(zero) altitude.
[0057] A set of specific range distances R.sub.1, R.sub.2, R.sub.3,
. . . , R.sub.K is chosen so that each range point R.sub.k
corresponds to one of the output points for the computations of
Equation (2). Then
R.sub.1=R.sub.Z+RDI
R.sub.2=R.sub.1+RDI
R.sub.3=R.sub.2+RDI
. . .
R.sub.K=R.sub.K-1+RDI (5)
in which, R.sub.K equals the maximum range distance for the
trajectory computation.
[0058] The sequence starts one range-distance increment (RDI)
beyond the zero-range distance R.sub.Z because the projectile
trajectory rises only a little above the line of sight at points
between the muzzle and the zero-range distance R.sub.Z. This is
because the zero-range distance R.sub.Z for the firearm is chosen
so that a target miss will not occur for a direct aim at a target
closer than R.sub.Z. For an "inclined target" elevated or depressed
relative to the firing point, the projectile trajectory is flatter
than it is for zero inclination, and no BPcorr is needed for target
distances less than R.sub.Z.
[0059] The computations of the equations of Equation (5) result in
a list of BPcorr values at each specified range distance R.sub.k
and at each altitude chosen for evaluation. The actual number of
such lists for each altitude is given by:
K = R k - R Z RDI ( 6 ) ##EQU00001##
[0060] At this point in the computations, a second-order, or at
most a third-order, polynomial is fitted to the BPcorr values
versus altitude in the list above resulting in a polynomial of the
form:
BPcorr(R.sub.k,alt)=c.sub.1k(R.sub.k)x(alt)+c.sub.2k(R.sub.k)x(alt).sup.-
2+c.sub.3k(R.sub.k)x(alt).sup.3 (7)
[0061] Equation (7) expresses the Bullet Path Height Correction
BPcorr at a specific range distance R.sub.k and any altitude (alt)
as a power series in which the coefficients c.sub.nk(R.sub.k)
change values at each specific range distance R.sub.k. The initial
value c.sub.0k(R.sub.k) usually appearing in the polynomial of
Equation (7) is always 0 because the Bullet Path Height Corrections
for zero altitude are zero at all range distances. If only a
second-order polynomial is necessary (which is usually the case),
then the third term on the right side of Equation (7) does not
appear. There would then be K such polynomials for a given
projectile. For the present example in which the maximum-range
distance R.sub.K is 800 yards, the zero range distance R.sub.Z is
200 yards, and the range-distance increment RDI is 50 yards, there
would be twelve polynomials of the form of Equation (7) to
characterize the BPcorr at 800, 750, 700, 650, . . . , down to 250
yards (or meters): That is,
K = 800 - 200 50 = 12. ( 8 ) ##EQU00002##
[0062] At this point, the calculations performed by the master
processor have been completed. The coefficients a.sub.ij in
Equation (2) and the K sets of coefficients c.sub.1(R), c.sub.2(R),
and c.sub.3(R) for Equation (7) are stored for later transfer to
the device processor at 607 at a convenient time.
[0063] Few shooters sight in exactly at sea level. A shooter
normally sights-in a firearm at a convenient location at some
altitude, referred to herein as the zero-point altitude
(alt.sub.ZP), which is almost always above sea level. Then, in the
field the shooter fires at a target at yet a different altitude,
referred to herein as firing-point altitude (alt.sub.FP) if the
shooter has a reference trajectory computed for sea level, two
Bullet Path Height corrections BPcorr are necessary to modify the
reference trajectory to predict the projectile impact point at the
field location:
[0064] The first correction modifies the sea level reference
trajectory to the altitude alt.sub.ZP at which the shooter sighted
in. The second correction modifies the reference trajectory for the
altitude alt.sub.FP at which the shooter must fire. It has been
determined that the net Bullet Path Height Correction BPcorr for
any two altitudes and any range distance to the target can be
computed from:
BPcorr(net)=BPcorr(R.sub.T,alt.sub.FP)-BPcorr(R.sub.T,alt.sub.ZP)
(9)
in which, R.sub.T is the target range distance with respect to the
firing point; [0065] BPcorr(R.sub.T,alt.sub.ZP) is the Bullet Path
Height correction BPcorr evaluated at alt.sub.ZP, the sighting-in
location altitude and target range distance R.sub.T, evaluated by
Equation (7) above; and [0066] BPcorr(R.sub.T, alt.sub.FP) is the
Bullet Path Height correction BPcorr evaluated at alt.sub.FP, the
firing point altitude, and the true target range distance R.sub.T
evaluated by Equation (7) above.
[0067] This crucial Equation (9) reflects an observation that the
net Bullet Path Height Correction for zeroing-in at a first
altitude and then firing at a second altitude is the negative of
the correction obtained for zeroing-in at the second altitude and
then firing at the first altitude. Thus, Equation (9) is correct
for all altitude situations.
[0068] The net Bullet Path Height Correction BPcorr(net) of
Equation (9) is applied to the original reference projectile
trajectory at range distance R.sub.T to calculate the correct
Bullet Path Height BPH for the target at the firing location.
[0069] Note that Equations (7) and (9) are evaluated for a
level-fire situation, as if the target were at a distance R.sub.T
in the same level plane as the muzzle of the firearm. The target
may in fad be inclined at some angle .alpha..sub.T (positive upward
or negative downward) relative to the firing point. It has been
shown in "Inclined Fire," W. T. McDonald, 2003, available from
sierrabullets.com, that the correct Bullet Path Height BPH for an
inclined target can be computed from the level-fire trajectory. The
appropriate equation is:
BPinclined(R.sub.T,.alpha..sub.T)=BPlevel(R.sub.T)cos
.alpha..sub.T-(1.0-cos
.alpha..sub.T)[h.sub.S+(R.sub.T/R.sub.Z)(D.sub.Z-h.sub.S)] (10)
[0070] in which, BPinelined(R.sub.T,.alpha..sub.T) is the Bullet
Path Height BPH for a target at straight line range distance
R.sub.T and inclination angle .alpha..sub.T on the inclined
trajectory; [0071] BPlevel(R.sub.T) is the Bullet Path Height BPH
computed as if the target were at the same range distance R.sub.T
in a level-fire situation; [0072] h.sub.S is the sight height above
the bore centerline (always positive for a sighting device mounted
above the bore); [0073] R.sub.Z is the zero range distance for the
firearm; and [0074] D.sub.Z is the Drop for the reference
trajectory at the zero range distance R.sub.Z (available from the
calculation of the reference trajectory in the master
processor).
[0075] Equation (10), when processed in a device-processor-type
computer processor, is an excellent approximation with accuracy
well within 1.0 minute of angle (MoA) for range distances within
the maximum effective range of high powered cartridges. Note that
R.sub.Z and D.sub.Z are fixed for a given projectile and are also
transferred from the master processor to the device processor. With
the definitions and equations above, the computations performed by
the device processor are little more than arithmetic. The
trigonometric cosine function must either be available in the
device processor, or a table of cosine values must be available fix
the device processor for angle range of 0 degrees to 70
degrees.
[0076] FIG. 7 depicts a flow diagram 700 for one exemplary
embodiment of operations and computational process performed by a
device processor for generating Altitude-Compensated Inclined
Shooting (AGES) trajectory information for a selected cartridge. In
one exemplary embodiment, results of the ACES trajectory
information computations performed by the master processor would
have been transferred to the device processor at 607 in FIG. 6. As
such, the computations performed by the master processor operations
need not occur in real time and could occur in a remote location in
advance of a user venturing into the field because the computations
depend only on well-known characteristics of the firearm and
ammunition and standard atmospheric conditions. The transferred
reference trajectory information comprises:
(1) the coefficients a.sub.ij of the reference trajectory Bullet
Path Height BPH from Equation (1); (2) the range distance
boundaries of the sectors i of the reference trajectory within
which specific a.sub.ij coefficients apply; (3) the list of BPcorr
coefficients c.sub.1k, c.sub.2k, and c.sub.3k for each of the k
range distance points R.sub.k; (4) the zero-range distance R.sub.Z
from Equation (10); (5) the projectile Drop at the zero-range
distance D.sub.Z from Equation (10); and (6) the sight height of
the firearm h.sub.S from Equation (10).
[0077] At 701, before venturing into the field, the field-dependent
data for generating Altitude-Compensated Inclined Shooting (ACIS)
trajectory information for a selected cartridge is input into the
device processor. In particular, the altitude at which the firearm
was sighted-in, alt.sub.ZP, and the altitude of the firing point in
the field, alt.sub.FP, are manually input the device processor. The
altitude alt.sub.ZP could be entered into the device processor when
the firearm is sighted-in, and then stored in, for example,
long-term memory associated with the device processor.
Alternatively, could be entered into the device processor when the
results of the computations performed by the master processor
information are transferred into the device processor. In either
case, alt.sub.ZP must be entered before computations can begin at
the firing point. The altitude of the firing point alt.sub.FP
normally is entered at the time of or just prior to, encounter with
a target at 702. In situations in which a shooter can predict where
the target encounter will take place, the firing point altitude
alt.sub.FP may be entered into the device processor prior to
venturing into the field. The subsequent calculations will be
accurate provided that the ultimate firing point does not
significantly depart (about .+-.300 feet AST) from the predicted
firing point when the target is encountered in the field.
[0078] At 703, when a target is encountered, the shooter initiates
ACIS trajectory computations. The device processor communicates
with sensors measuring the direct (straight line) target range
distance R.sub.T (i.e., from a rangefinder) at 703a, and the target
inclination angle .alpha..sub.T (i.e., from an inclinometer) at
703b. This communication may take place either (1) automatically
electronically, or (2) via manual input by the shooter.
[0079] At 704, the device processor computes the Bullet Path Height
BPH values for the target-range distance R.sub.T on a level-fire
trajectory using the polynomial Equation (2) with the values of the
coefficients a.sub.ij transferred from the master processor at 607
in FIG. 6. The device processor first determines the trajectory
sector i in which the target lies by comparing R.sub.T with the
range distance boundaries transferred from the master processor,
then selecting the set of a.sub.ij coefficients for that sector to
perform the computations.
[0080] In the situation in which the device processor has limited
numerical precision, Equation (2) can be reformulated as a "nested
polynomial" for the evaluation computations in the following
form:
BP(R.sub.T)=a.sub.i0A.sub.1
A.sub.1=1+(a.sub.i1/a.sub.i0)R.sub.TA.sub.2
A.sub.2=1+(a.sub.i2/a.sub.i1)R.sub.TA.sub.3
A.sub.3=1+(a.sub.i3/a.sub.i2)R.sub.TA.sub.4
A.sub.4=1+(a.sub.i4/a.sub.i3)R.sub.TA.sub.5
A.sub.5=1+(a.sub.i5/a.sub.i4)R.sub.TA.sub.6
A.sub.6=1+(a.sub.i6/a.sub.i5)R.sub.TA.sub.7
A.sub.7=1+(a.sub.i7/a.sub.i6)R.sub.T (11)
[0081] The computation of BP(R.sub.T) begins with the calculation
of A.sub.7, then proceeds to A.sub.6, then to A.sub.5, and so
forth, to the final calculation of BP(R.sub.T). Each computation
includes a truncation error based on the limited numerical
precision of the device processor. Accordingly, in the calculation
sequence of Equation (11), truncation errors occur systematically
from the smallest numerical result to the largest, so that overall
truncation error in BP(R.sub.T) is thereby minimized. The sequence
of Equation (11) also limits the number of multiplications that are
performed because R.sub.T is not raised to powers greater than 1 in
any calculation.
[0082] At 705, the device processor calculates the (fully
corrected) BPcorr for a target at range distance R.sub.T for a
level-fire trajectory by first determining between which pair of
specific range distances, R.sub.k-1 and R.sub.k the value R.sub.T
lies by, for example, the following sequence of tests:
Is R.sub.T>R.sub.1? If no, then R.sub.k-1=R.sub.Z, and
R.sub.k=R.sub.1. If yes, then:
Is R.sub.T>R.sub.2? If no, then R.sub.k-1=R.sub.1, and
R.sub.k=R.sub.2. If yes, then:
Is R.sub.T>R.sub.3? If no, then R.sub.k-1=R.sub.2, and
R.sub.k=R.sub.3. If yes, then:
. . .
Is R.sub.T>R.sub.K-1?If no, then R.sub.k-1=R.sub.K-2, and
R.sub.k=R.sub.K-1. If yes, then:
R.sub.k-1=R.sub.K-1, and R.sub.k=R.sub.K. (12)
[0083] Note that the sequence of tests of Equation (12) presumes
that (a) no target-range distance is less than the zero-range
distance R.sub.Z (if so, the shooter will simply fire directly at
the target), and (b) that no target-range distance is greater than
the maximum range distance R.sub.K specified for the firearm. If
necessary, tests can be incorporated in the device processor
software to assure that these two presumptions are true.
[0084] With the specific range distances R.sub.k-1 and R.sub.k
known between which R.sub.T lies, at 706 the device processor next
computes the Bullet Path Height Correction BPcorr(R.sub.k-1,
alt.sub.ZP) at range distance R.sub.k-1 and the altitude alt.sub.ZP
at which the firearm was sighted in. This computation uses Equation
(7) and the list of the coefficients c.sub.1k, c.sub.2k, and
c.sub.3k transferred from the master processor. If necessary to
preserve computational precision in the device processor, Equation
(7) may be reformulated as a nested polynomial using the procedure
outlined for Equation (11). Computation as a nested polynomial is
directly followed by the computation of the Bullet Path Height
Correction BPcorr(R.sub.k,alt.sub.ZP) at the specific range
distance R.sub.k and the altitude alt.sub.ZP at which the firearm
was sighted in. Then, because R.sub.T lies between R.sub.k-1 and
R.sub.k, the BPcorr(R.sub.k, alt.sub.ZP) is computed by linear
interpolation:
BPcorr ( R T , alt ZP ) = BPcoor ( R k - 1 , alt ZP ) + R T - R k -
1 R k - R k - 1 [ BPcorr ( R k , alt ZP ) - BPcorr ( R k - 1 , alt
ZP ) ] ( 13 ) ##EQU00003##
[0085] The device processor also computes at 705
BPcorr(R.sub.k,alt.sub.FP) at the target range distance R.sub.T and
the firing point altitude alt.sub.FP using the same procedure as
for Equation (13), thereby yielding:
BPcorr ( R T , alt FP ) = BPcorr ( R k - 1 , alt FP ) + R T - R k -
1 R k - R k - 1 [ BPcorr ( R k , alt FP ) - BPcorr ( R k - 1 , alt
FP ) ] ( 14 ) ##EQU00004##
[0086] At 706, the net Bullet Path Height Correction is calculated
using Equation (9) above:
BPcorr(net)=BPcorr(R.sub.T,alt.sub.FP)-BPcorr(R.sub.T,alt.sub.ZP)
(15)
[0087] At this point, the result of Equation (15) is the net Bullet
Path Height Correction for a firearm and cartridge zeroed-in at an
altitude alt.sub.ZP and then fired at an altitude alt.sub.FP at a
fictitious or theoretical target situated at a range distance
R.sub.T in a plane level with the firing point. At 707, the net
correction BPcorr(net) is added to the Bullet Path Height
BP(R.sub.T) computed earlier for the target; range distance R from
the range-distance sensor shown in FIG. 7. That is:
BPlevel(R.sub.T)=BP(R.sub.T)+BPcorr(net) (16)
At 708, the final computation in the device processor adjusts the
result of Equation (16) for an inclined target at the same distance
R.sub.T and inclination angle .alpha..sub.T relative to the firing
point. The final result is:
BPinclined ( R T , .alpha. T ) = BPlevel ( R T ) x cos .alpha. T -
( 1 - cos .alpha. T ) [ h s + R T R Z ( D Z - h s ) ] ( 17 )
##EQU00005##
[0088] It remains only for the device processor to display the ACIS
holdover information to the shooter at 709. The holdover will be
the negative of the adjusted Bullet Path Height BPH for the
inclined target because, because the projectile will be below the
line of sight at range distances beyond the zero-range distance
R.sub.Z, the shooter must aim high by an equivalent deflection at
the target. Elevation adjustments may be made by the shooter based
on the displayed ACIS information.
[0089] A skilled mathematician will note that alternative
mathematical implementations may be used to accomplish the detailed
computations described above. All such alternatives are included
herein. It is imperative, however, that the two crucial
characteristics of this computation method be preserved by whatever
mathematical implementation is used. The first characteristic is
that the same zeroing-in range distance R.sub.Z is used at all
altitudes. This is a practical convenience to the shooter as well
as essential to the mathematics; the shooter need not attempt to
adjust the zeroing-in operations for the altitude of the zeroing-in
location. The second characteristic is the use of Equation (9) to
compute the net Bullet Path Height Correction IsTcorr to add to the
Bullet Path Height value on the reference trajectory at target
range distance R.sub.T.
[0090] The above-described methods may be implemented in a
portable, handheld laser rangefinder 800, an exemplary embodiment
of which is depicted in FIG. 8. The exemplary embodiment of
rangefinder 800 includes a laser ranging system 804 having a lens
806 through which a laser beam is emitted and reflected laser light
is received for determining a range to a distant target.
Rangefinder 800 also includes an integrated optical targeting sight
810 comprising an objective 812 and an eyepiece 814, through which
a user views the target. In one exemplary embodiment, rangefinder
800 comprises a power button 816 that turns on certain electronics
of rangefinder 800 and causes rangefinder 800 to emit laser pulses
and acquire range readings. A pair of menu interface buttons 818
may be provided on rangefinder 800 for operating menus for
inputting setup information and enabling functions of the
rangefinder, similar to that described in U.S. Patent Application
Publication No. 2007/0097351 A1 to York et al., the disclosure of
which is incorporated herein by reference. It should be understood
that other alternative exemplary embodiments of a portable handheld
laser rangefinder are possible.
[0091] FIG. 9 depict one view of elements of an exemplary display
900 which, in one exemplary embodiment of rangefinder 800, may be
placed in the field of view of the targeting sight 810 of
rangefinder 800. In one exemplary embodiment, display 900 comprises
a transmissive LCD display panel placed between objective 812 and
eyepiece 814. Other display devices, however, may be used,
including displays generated outside of the optical path of the
targeting sight 810 and injected into the optical path of the
targeting sight 810, such as by projecting a reticle display onto a
prism or beam-combining element (reverse beam splitter). In one
exemplary embodiment, display 900 may comprise a circular menu 904
along its perimeter, which can be navigated using buttons 816, 818
to select one or more of various functions of rangefinder 800. The
exemplary icons labeled >150, 1st TGT, LAST TGT, M/FT/YD, LOS
relate to ranging functions and/or modes of display. In one
exemplary embodiment, the exemplary TBR icon may stand for TRUE
BALLISTIC RANGE and, when selected, activates calculation methods
for determining ACIS holdover or the Equivalent Horizontal Range
(also known as the TRUE BALLISTIC RANGE). In one exemplary
embodiment, the exemplary icon for BOW toggles between bullet
calculations (FIGS. 4, 6 and 7) and arrow calculation (FIG. 5), and
between ballistic groupings for bullets and arrows, which are
selectable from the menu segments of the exemplary A/B/C menu
icon.
[0092] One exemplary embodiment of display 900 may also comprise a
data display 910 including a primary data display section 902 and a
secondary data display section 904. Primary data display section
902 may be used to output EHR calculations, as indicated by the
adjacent exemplary icon labeled "TBR". Secondary numerical display
904 may be used to output the LOS range, as indicated by the
adjacent exemplary icon labeled "LOS". A third data display section
906 may be provided for displaying an inclination angle, measured
by an inclinometer sensor 1008 (FIG. 10) of rangefinder 800. Still
further exemplary display sections may be provided for displaying
data representative of a trajectory parameter, such as ballistic
path height BP, vertical ballistic drop, ACIS information, energy,
momentum, velocity, etc., at the target range. In one exemplary
embodiment, based on ballistic path height BP or another trajectory
parameter TP, another display section (not shown) may display a
recommended holdover adjustment in inches, millimeters or mils, at
the target range or a recommended elevation adjustment in MOA or
mils.
[0093] A battery power indicator 908 may be included in exemplary
display 900 for indicating an estimate of the amount of battery
power remaining. One or more display, segments 909 in the center of
the battery power indicator 908 may be turned of to indicate the
remaining battery power. A user-configurable targeting reticle
display 910 may also be included in exemplary display 900 for
facilitating aiming of rangefinder 800. In one exemplary
embodiment, exemplary reticle display 910 comprises a plurality of
segments that allow exemplary reticle display 910 to be
reconfigured in various ways.
[0094] FIG. 110 depicts an exemplary block diagram for an exemplary
embodiment of rangefinder device 1000 according to the subject
matter disclosed herein. In one exemplary embodiment, rangefinder
device 1000 could be configured similar to the exemplary portable,
handheld rangefinder device depicted in FIG. 8. In another
exemplary embodiment, rangefinder device 1000 could be configured
to be part of or communicatively coupled to an exemplary telescopic
sighting device 1100 depicted in FIG. 11. Rangefinder device 1000
comprises a computer processor or digital processor 1001, such as a
microprocessor or digital signal processor (DSP), operatively
coupled to laser ranging system 1002, display device 1003, and user
interface 1004, 1005. Targeting sight 1006 and laser ranging system
1002 are aligned relative to each other and are supported in a
common housing 1007, which may include an internal carriage or
frame. An inclinometer sensor 1008 is mounted to a support
structure in rangefinder device 1000 in alignment with ranging
system 1002 and targeting sight 1006 for measuring the inclination
angle .theta. of the line of sight (LOS) between a vantage point VP
and a target T (FIG. 2). The ballistic calculations described above
with reference to FIGS. 1-7 may be performed by digital processor
1001 of rangefinder device 1000 automatically after a laser ranging
measurement has been made by ranging system 1002.
[0095] To facilitate accurate ballistics calculations, digital
processor 1001 is in communication with inclinometer 1008 and other
sensors, such as an electronic compass 1009, a temperature sensor
1010, a barometer/altimeter sensor 1011, and/or a relative humidity
sensor 1012. The data from the sensors may be used as
shooting-condition inputs to ballistic calculation software
operating on digital processor 1001 for performing the methods
described above with reference to FIGS. 1-7. In one exemplary
embodiment, a memory 1013 readable by digital processor 1001 stores
a software program, sensor data, and/or user-defined settings,
among other information. In one exemplary embodiment, memory 1013
may also store data tables including ballistic coefficients for
various bullets and arrows or groups thereof. In another exemplary
embodiment, memory 1013 may store data tables including ballistic
tables with predicted trajectory parameters for known shooting
conditions (including a range of angles) and tables with EHR data
(under level-fire conditions) for a range of trajectory parameters.
A GPS receiver 1014 and antenna 1015 for acquiring geographic
location data from GPS satellite signals may also be included in
rangefinder device 1000 in operative association with digital
processor 1001. A signaling module 1016, which may include an
antenna 1017, may be coupled to digital processor 1001 for
transmitting signals representative of ballistic calculation data
calculated by digital processor 1001, such as one or more
trajectory parameters, EHR, elevation adjustments and ACIS holdover
adjustments.
[0096] The output of BR, EHR or ACIS information may be displayed
via a graphical representation of a corresponding aiming mark of a
weapon aiming device reticle or targeting sight. In one exemplary
embodiment of such a display method, an aiming mark of the
facsimile reticle corresponding to the output BP, EHR or ACIS data
is identified by highlighting, emphasizing, flashing, coloring, or
otherwise changing the appearance of the aiming mark to accomplish
a graphical display of the recommended aiming point in relation to
the overall reticle pattern. The graphical display communicates to
the user which of several aiming marks or points on the
corresponding riflescope reticle would be recommended for use in
holdover aiming of a firearm that is separate from the rangefinder.
In another exemplary embodiment, rangefinder device 1000 and a
targeting sight are integrated in a common housing with a
riflescope or other weapon aiming device, in which the same
sighting device and reticle display may be used for aiming
rangefinder device 1000 and for aiming the projectile weapon
utilizing a graphical holdover aiming display. In still another
exemplary embodiment, BR, EHR or ACIS data may be transmitted via
wires or wirelessly by signaling module 1016 and antenna 1017 of
rangefinder device 1000 for receipt by a riflescope or other aiming
device, and subsequent display using a graphical display.
Presenting EHR, BP or ACIS information in a graphical display that
is a facsimile of reticle of a weapon aiming device may help avoid
human errors that could otherwise result from attempting to
manually convert numerical BP, EHR or ACIS data or using it to
manually determine which of several secondary aiming marks of a
riflescope reticle should be used to aim the weapon.
[0097] With reference to FIGS. 10 and 11, signaling module 1016 and
antenna 1017 of rangefinder device 1000 may be configured to send
radio frequency signals to riflescope 1100 mounted on a firearm
1104 or to another weapon aiming device (not shown). Radio signals
may be used to wirelessly feed or control a reticle display (not
shown) of riflescope 1100 viewable through a riflescope eyepiece
1114 for displaying ballistics data in the field of view and/or for
other purposes. Wireless data transmission enables rangefinder
device 1000 to be separate from the firearm and protected from the
effects of recoil and other harsh environmental conditions to which
riflescopes are typically exposed. For example, rangefinder device
1000 may be held by a first person, such as a spotter, positioned
several meters away from a shooter holding a rifle 1104 with a
riflescope 1100 that receives data wirelessly from rangefinder
device 1000. Rangefinder device 1000 may also transmit data
wirelessly to several different riflescopes or other devices
substantially simultaneously, allowing a single spotter to provide
data to a group of shooters.
[0098] In one exemplary embodiment, the signals transmitted by
signaling module 1016 may include information representative of
elevation adjustments to be made in riflescope 1100 (in minutes of
angle (MOA) or fractional minutes of angle, such as 1/4 MOA or 1/2
MOA) based on ballistics calculations made by digital processor
1001. Elevation adjustments expressed in MOA or fractions thereof
may be displayed in the reticle of riflescope 1100 and/or be
effected via a manual adjustment of an elevation adjustment knob
1120, a motorized elevation adjustment mechanism, or by controlling
or shifting a reticle display or a reticle of riflescope 1100 for
offsetting an aiming mark in the amount of aiming adjustment
needed, or to show, highlight, or emphasize a fixed or ephemeral
aiming mark corresponding to the EHR or ACIS information calculated
by digital processor 1001. The kind of data needed to make such an
adjustment or aiming mark may depend on whether the riflescope
reticle is in the front focal plane or the rear focal plane of
riflescope 1100.
[0099] When a recommended elevation adjustment is displayed (in MOA
or otherwise) in the reticle display of riflescope 1100, the
recommended elevation adjustment may be updated dynamically as the
user manually adjusts an elevation setting of riflescope 1100, for
example, via an elevation adjustment knob 1120. To enable the
recommended elevation adjustment display to be updated dynamically,
the elevation adjustment knob 1120 may include a rotary encoder
that provides feedback to a display controller of riflescope 1100
or to digital processor 1001. Dynamic updating of the recommended
elevation adjustment may enable a reticle display to depict the
amount of adjustment remaining (e.g., remaining MOA or clicks of
the adjustment knob needed) as the user adjusts elevation, without
requiring constant communication between riflescope 1100 and
rangefinder device 1000 during the elevation adjustment process.
Dynamic updating of the remaining adjustment needed may facilitate
operation of rangefinder device 1000 and riflescope 1100
sequentially by a single person. In another exemplary embodiment,
rangefinder device 1000 may communicate constantly with riflescope
1100, which may allow two people (e.g., a shooter working with a
spotter) to more quickly effect accurate aiming adjustments.
[0100] In one exemplary embodiment, signaling module 1016 may
include an infrared transceiver, Bluetooth.TM. transceiver, or
other short-range low-power transceiver for communication with a
corresponding transceiver of riflescope 1100, for enabling two-way
communication while conserving battery power in rangefinder device
1000 and riflescope 1100. Data for controlling a reticle and/or
elevation adjustment mechanism 1120 may be transmitted via
Bluetooth or other radio-frequency signals. Also, because
Bluetooth.TM. transceivers facilitate two-way communication, the
rangefinder device 1000 may query riflescope 1100 for a current
elevation adjustment setting, a power adjustment setting, and other
information, such as the type of riflescope 1100 and reticle used.
This data may then be taken into account in ballistics calculations
performed by digital processor 1001. Elevation adjustment and power
adjustment settings of riflescope 1100 may be determined, for
example, by rotary position sensor/encoders associated with
elevation adjustment knob 1120 and power adjustment ring 1130.
[0101] In another exemplary embodiment, signaling module 1016 may
comprise a cable connector plug or socket for establishing a wired
connection to riflescope 1100. A wired connection may avoid the
need to have delicate electronics and battery power onboard
riflescope 1100. Wired and wireless connections may also be made
between signaling module 1016 and other devices, such as bow-sights
(including illuminated pin sights and others), PDAs, laptop
computers, remote sensors, data loggers, wireless data and
telephone networks, and others, for data collection and other
purposes.
[0102] Holdover indication in a riflescope, bow sight, or other
optical aiming device may be achieved by emphasizing an aiming mark
of the sight that corresponds to the EHR or ACIS information
calculated by rangefinder device 1000. In an exemplary ballistic
reticle, a primary aiming mark, which may be formed by the
intersection or convergence of a primary vertical aiming line with
a primary horizontal aiming line, coincides with a reference
sighted-in range (such as 200 yards horizontal). As described above
and in U.S. Pat. No. 7,603,804 B2 to Zaderey et al., titled
"Ballistic Reticle for Projectile Weapon Aiming Systems and Method
of Aiming," the disclosure of which is incorporated herein by
reference, secondary aiming marks are spaced along a primary
vertical aiming line and identify holdover aiming points at which
bullet impact will occur at incremental ranges beyond the
sighted-in range.
[0103] Although the foregoing disclosed subject matter has been
described in some detail for purposes of clarity of understanding,
it will be apparent that certain changes and modifications may be
practiced that are within the scope of the appended claims.
Accordingly, the present embodiments are to be considered as
illustrative and not restrictive, and the subject matter disclosed
herein is not to be limited to the details given herein, but may be
modified within the scope and equivalents of the appended
claims.
* * * * *